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Responder Trials

Preprocessing Summary
Number of Subjects
Responder Trials (Sample A)
Overt Attention Data
Total Participants Excluded (Sample A) Participants Included (Sample A) Observations Lost (< 90% Valid Gaze Samples) Observations Lost (NA for CorrectIncorrect) NA Rows for FileName NA Rows for rRTsacc Trials with Incorrect Response Observations Lost (NA for PredictiveGazeFace Observations Lost with SRT <0.15s & > 3s)
86 22 64 553 0 0 1048 92 0 1442
Summary (Trials Retained, Sample A)
Accuracy Data
Overt Attention Data
SRT Data
Trials Lost Due to Poor Calibration
Belief Mean (%) SD (%) Mean (%) SD (%) Mean (%) SD (%) Mean (%) SD (%)
AI 81.99588 21.18553 81.99588 21.18553 63.78601 20.35482 7.690329 15.852073
Human 82.20721 16.19655 82.20721 16.19655 67.39865 17.01739 5.048799 9.181748

Accuracy

Plot

Generalised Linear Mixed Effect Model for Responder Accuracy

Estimate Std. Error z value Pr(>|z|)
(Intercept) 7.669 0.723 10.608 0.000
CongruencyIncongruent -4.630 0.718 -6.453 0.000
BeliefHuman 1.527 0.665 2.295 0.022
AvatarRobot 1.973 0.589 3.349 0.001
CongruencyIncongruent:BeliefHuman -0.847 0.721 -1.175 0.240
CongruencyIncongruent:AvatarRobot -1.485 0.778 -1.908 0.056
BeliefHuman:AvatarRobot -1.380 0.927 -1.489 0.137
CongruencyIncongruent:BeliefHuman:AvatarRobot 1.042 1.205 0.865 0.387
##                                   (Intercept) 
##                                     7.6693093 
##                         CongruencyIncongruent 
##                                    -4.6304260 
##                                   BeliefHuman 
##                                     1.5266551 
##                                   AvatarRobot 
##                                     1.9732340 
##             CongruencyIncongruent:BeliefHuman 
##                                    -0.8467675 
##             CongruencyIncongruent:AvatarRobot 
##                                    -1.4850553 
##                       BeliefHuman:AvatarRobot 
##                                    -1.3801848 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                     1.0416062
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: CorrectIncorrect ~ Congruency + Belief + Avatar + Congruency:Belief +  
##     Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar +  
##     (1 | SubjectID) + (1 | TrialID)
##    Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
##      AIC      BIC   logLik deviance df.resid 
##    691.4    760.4   -335.7    671.4     7317 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -28.5913   0.0131   0.0344   0.0630   1.4709 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  TrialID   (Intercept) 8.194    2.862   
##  SubjectID (Intercept) 2.390    1.546   
## Number of obs: 7327, groups:  TrialID, 72; SubjectID, 64
## 
## Fixed effects:
##                                               Estimate Std. Error z value
## (Intercept)                                     7.6693     0.7229  10.608
## CongruencyIncongruent                          -4.6304     0.7176  -6.453
## BeliefHuman                                     1.5267     0.6654   2.295
## AvatarRobot                                     1.9732     0.5892   3.349
## CongruencyIncongruent:BeliefHuman              -0.8468     0.7205  -1.175
## CongruencyIncongruent:AvatarRobot              -1.4851     0.7784  -1.908
## BeliefHuman:AvatarRobot                        -1.3802     0.9270  -1.489
## CongruencyIncongruent:BeliefHuman:AvatarRobot   1.0416     1.2045   0.865
##                                               Pr(>|z|)    
## (Intercept)                                    < 2e-16 ***
## CongruencyIncongruent                          1.1e-10 ***
## BeliefHuman                                   0.021762 *  
## AvatarRobot                                   0.000811 ***
## CongruencyIncongruent:BeliefHuman             0.239896    
## CongruencyIncongruent:AvatarRobot             0.056410 .  
## BeliefHuman:AvatarRobot                       0.136509    
## CongruencyIncongruent:BeliefHuman:AvatarRobot 0.387176    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.538                                          
## BeliefHuman -0.360  0.116                                   
## AvatarRobot -0.079  0.108  0.135                            
## CngrncyI:BH  0.151 -0.420 -0.478 -0.139                     
## CngrncyI:AR  0.118 -0.387 -0.096 -0.745  0.332              
## BlfHmn:AvtR  0.051 -0.067 -0.368 -0.635  0.344  0.473       
## CngrI:BH:AR -0.076  0.220  0.267  0.480 -0.586 -0.642 -0.763
## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict CorrectIncorrect with Congruency, Belief and Avatar (formula:
## CorrectIncorrect ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar). The model
## included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.84) and the part related to the fixed effects alone (marginal R2) is of 0.32.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 7.67 (95% CI [6.25, 9.09], p < .001). Within
## this model:
## 
##   - The effect of Congruency [Incongruent] is statistically significant and
## negative (beta = -4.63, 95% CI [-6.04, -3.22], p < .001; Std. beta = -4.63, 95%
## CI [-6.04, -3.22])
##   - The effect of Belief [Human] is statistically significant and positive (beta
## = 1.53, 95% CI [0.22, 2.83], p = 0.022; Std. beta = 1.53, 95% CI [0.22, 2.83])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 1.97, 95% CI [0.82, 3.13], p < .001; Std. beta = 1.97, 95% CI [0.82, 3.13])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.85, 95% CI [-2.26, 0.57], p = 0.240;
## Std. beta = -0.85, 95% CI [-2.26, 0.57])
##   - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -1.49, 95% CI [-3.01, 0.04], p = 0.056;
## Std. beta = -1.49, 95% CI [-3.01, 0.04])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -1.38, 95% CI [-3.20, 0.44], p = 0.137;
## Std. beta = -1.38, 95% CI [-3.20, 0.44])
##   - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and positive (beta = 1.04, 95% CI [-1.32, 3.40],
## p = 0.387; Std. beta = 1.04, 95% CI [-1.32, 3.40])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.
## The model included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 | TrialID))
## [1] "very strong evidence against"
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Independent Samples t-Test (Accuracy by Belief)

The mean Accuracy in the AI group was 97.486 (SD = 5.559), whereas the mean in the Human group was 98.842 (SD = 2.933). A Welch two-samples t-test showed that the difference was statistically significant, t(74.4904527) = -1.6334224, p = 0.107.

Influence of CATI Scores on Accuracy

## 
##  Shapiro-Wilk normality test
## 
## data:  AccuracyCATI$Diff_ProportionCorrect[0:5000]
## W = 0.62301, p-value = 2.676e-16
## 
##  Shapiro-Wilk normality test
## 
## data:  AccuracyCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155
## [1] 3.7e-24
## [1] 0.4711401

##                               CATI Diff_ProportionCorrect
## CATI                    1.00000000            -0.05435454
## Diff_ProportionCorrect -0.05435454             1.00000000

## 
##  Spearman's rank correlation rho
## 
## data:  AccuracyCATI$Diff_ProportionCorrect and AccuracyCATI$CATI
## S = 320188, p-value = 0.7216
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##         rho 
## -0.03245308

Accuracy Summary

## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

Overt Attention

Plot

Generalised Linear Mixed Effect Model for Responder Overt Attention

Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.119 0.292 -0.406 0.684
CongruencyIncongruent 1.029 0.182 5.663 0.000
BeliefHuman 0.598 0.378 1.582 0.114
AvatarRobot 0.578 0.105 5.498 0.000
CongruencyIncongruent:BeliefHuman -0.022 0.202 -0.111 0.912
CongruencyIncongruent:AvatarRobot 0.015 0.221 0.067 0.946
BeliefHuman:AvatarRobot -0.144 0.137 -1.052 0.293
CongruencyIncongruent:BeliefHuman:AvatarRobot -0.153 0.296 -0.517 0.605
##                                   (Intercept) 
##                                   -0.11883371 
##                         CongruencyIncongruent 
##                                    1.02940923 
##                                   BeliefHuman 
##                                    0.59819149 
##                                   AvatarRobot 
##                                    0.57784605 
##             CongruencyIncongruent:BeliefHuman 
##                                   -0.02234746 
##             CongruencyIncongruent:AvatarRobot 
##                                    0.01489097 
##                       BeliefHuman:AvatarRobot 
##                                   -0.14438411 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                   -0.15327107
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: 
## PredictiveGazeFace ~ Congruency + Belief + Avatar + Congruency:Belief +  
##     Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar +  
##     (1 | SubjectID) + (1 | TrialID)
##    Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   7314.1   7383.1  -3647.1   7294.1     7317 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.2636 -0.5737  0.3112  0.5663  7.1014 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev.
##  TrialID   (Intercept) 0.1407   0.3751  
##  SubjectID (Intercept) 2.0842   1.4437  
## Number of obs: 7327, groups:  TrialID, 72; SubjectID, 64
## 
## Fixed effects:
##                                               Estimate Std. Error z value
## (Intercept)                                   -0.11883    0.29242  -0.406
## CongruencyIncongruent                          1.02941    0.18177   5.663
## BeliefHuman                                    0.59819    0.37812   1.582
## AvatarRobot                                    0.57785    0.10510   5.498
## CongruencyIncongruent:BeliefHuman             -0.02235    0.20184  -0.111
## CongruencyIncongruent:AvatarRobot              0.01489    0.22099   0.067
## BeliefHuman:AvatarRobot                       -0.14438    0.13728  -1.052
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.15327    0.29627  -0.517
##                                               Pr(>|z|)    
## (Intercept)                                      0.684    
## CongruencyIncongruent                         1.49e-08 ***
## BeliefHuman                                      0.114    
## AvatarRobot                                   3.84e-08 ***
## CongruencyIncongruent:BeliefHuman                0.912    
## CongruencyIncongruent:AvatarRobot                0.946    
## BeliefHuman:AvatarRobot                          0.293    
## CongruencyIncongruent:BeliefHuman:AvatarRobot    0.605    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.144                                          
## BeliefHuman -0.750  0.074                                   
## AvatarRobot -0.168  0.275  0.130                            
## CngrncyI:BH  0.086 -0.615 -0.112 -0.247                     
## CngrncyI:AR  0.075 -0.553 -0.058 -0.452  0.499              
## BlfHmn:AvtR  0.128 -0.210 -0.167 -0.765  0.316  0.346       
## CngrI:BH:AR -0.056  0.412  0.073  0.337 -0.671 -0.746 -0.445
## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict PredictiveGazeFace with Congruency, Belief and Avatar (formula:
## PredictiveGazeFace ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar). The model
## included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.43) and the part related to the fixed effects alone (marginal R2) is of 0.05.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at -0.12 (95% CI [-0.69, 0.45], p = 0.684). Within
## this model:
## 
##   - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.03, 95% CI [0.67, 1.39], p < .001; Std. beta = 1.03, 95% CI
## [0.67, 1.39])
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.60, 95% CI [-0.14, 1.34], p = 0.114; Std. beta = 0.60, 95% CI [-0.14,
## 1.34])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.58, 95% CI [0.37, 0.78], p < .001; Std. beta = 0.58, 95% CI [0.37, 0.78])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.02, 95% CI [-0.42, 0.37], p = 0.912;
## Std. beta = -0.02, 95% CI [-0.42, 0.37])
##   - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.01, 95% CI [-0.42, 0.45], p = 0.946;
## Std. beta = 0.01, 95% CI [-0.42, 0.45])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.14, 95% CI [-0.41, 0.12], p = 0.293;
## Std. beta = -0.14, 95% CI [-0.41, 0.12])
##   - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.15, 95% CI [-0.73, 0.43],
## p = 0.605; Std. beta = -0.15, 95% CI [-0.73, 0.43])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.
## The model included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 | TrialID))
## [1] "very strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.01333238
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Influence of CATI Scores on Overt Attention

## 
##  Shapiro-Wilk normality test
## 
## data:  PredictiveGazeFaceCATI$Diff_PredictiveGazeFaceMean[0:5000]
## W = 0.9649, p-value = 0.002602
## 
##  Shapiro-Wilk normality test
## 
## data:  PredictiveGazeFaceCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155
## [1] 0.001458021
## [1] 0.4711401

##                                   CATI Diff_PredictiveGazeFaceMean
## CATI                         1.0000000                  -0.1264442
## Diff_PredictiveGazeFaceMean -0.1264442                   1.0000000

## 
##  Spearman's rank correlation rho
## 
## data:  PredictiveGazeFaceCATI$Diff_PredictiveGazeFaceMean and PredictiveGazeFaceCATI$CATI
## S = 359087, p-value = 0.1498
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.1300937

Overt Attention Summary

## [1] TRUE
## [1] TRUE

Saccadic Reaction Time (SRT)

Plot

Load Data and Identify Factors
All Trials

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Overt Attention Trials Only

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

No Overt Attention Trials Only

## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.

Linear Mixed Effects Models

Load Data and Identify Factors
All Trials
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 449.525 16.667 125.270 26.971 0.000
CongruencyIncongruent 70.442 25.999 97.872 2.709 0.008
BeliefHuman 25.317 15.835 61.794 1.599 0.115
AvatarRobot 65.592 13.405 61.246 4.893 0.000
CongruencyIncongruent:BeliefHuman -2.543 16.134 61.278 -0.158 0.875
CongruencyIncongruent:AvatarRobot -23.568 17.583 62.348 -1.340 0.185
BeliefHuman:AvatarRobot 20.722 17.230 59.677 1.203 0.234
CongruencyIncongruent:BeliefHuman:AvatarRobot 3.561 22.752 60.966 0.157 0.876
##                                   (Intercept) 
##                                    449.524721 
##                         CongruencyIncongruent 
##                                     70.442123 
##                                   BeliefHuman 
##                                     25.317308 
##                                   AvatarRobot 
##                                     65.591614 
##             CongruencyIncongruent:BeliefHuman 
##                                     -2.543341 
##             CongruencyIncongruent:AvatarRobot 
##                                    -23.567755 
##                       BeliefHuman:AvatarRobot 
##                                     20.721743 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                      3.561040
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 20.510 0.293 127.491 70.033 0.000
CongruencyIncongruent 1.183 0.453 90.113 2.612 0.011
BeliefHuman 0.434 0.271 61.993 1.602 0.114
AvatarRobot 0.986 0.204 61.755 4.831 0.000
CongruencyIncongruent:BeliefHuman -0.030 0.241 61.462 -0.126 0.900
CongruencyIncongruent:AvatarRobot -0.406 0.261 62.021 -1.554 0.125
BeliefHuman:AvatarRobot 0.346 0.262 60.216 1.322 0.191
CongruencyIncongruent:BeliefHuman:AvatarRobot -0.013 0.338 60.721 -0.038 0.970
##                                   (Intercept) 
##                                   20.50990171 
##                         CongruencyIncongruent 
##                                    1.18321626 
##                                   BeliefHuman 
##                                    0.43398897 
##                                   AvatarRobot 
##                                    0.98605884 
##             CongruencyIncongruent:BeliefHuman 
##                                   -0.03036783 
##             CongruencyIncongruent:AvatarRobot 
##                                   -0.40594273 
##                       BeliefHuman:AvatarRobot 
##                                    0.34631018 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                   -0.01288491
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief + Congruency:Avatar +  
##     Belief:Avatar + Congruency:Belief:Avatar + (0 + Congruency +  
##     Avatar + Congruency:Avatar | SubjectID) + (1 | TrialID)
##    Data: SRTData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 27621.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8040 -0.5996 -0.0064  0.5840  7.1527 
## 
## Random effects:
##  Groups    Name                              Variance Std.Dev. Corr       
##  TrialID   (Intercept)                       2.2968   1.5155              
##  SubjectID CongruencyCongruent               0.9437   0.9714              
##            CongruencyIncongruent             1.3258   1.1514    0.92      
##            AvatarRobot                       0.6296   0.7935   -0.04  0.09
##            CongruencyIncongruent:AvatarRobot 0.3683   0.6069   -0.45 -0.55
##  Residual                                    5.8429   2.4172              
##       
##       
##       
##       
##       
##  -0.39
##       
## Number of obs: 5885, groups:  TrialID, 72; SubjectID, 64
## 
## Fixed effects:
##                                                Estimate Std. Error        df
## (Intercept)                                    20.50990    0.29286 127.49130
## CongruencyIncongruent                           1.18322    0.45308  90.11270
## BeliefHuman                                     0.43399    0.27086  61.99300
## AvatarRobot                                     0.98606    0.20411  61.75516
## CongruencyIncongruent:BeliefHuman              -0.03037    0.24109  61.46155
## CongruencyIncongruent:AvatarRobot              -0.40594    0.26127  62.02111
## BeliefHuman:AvatarRobot                         0.34631    0.26205  60.21595
## CongruencyIncongruent:BeliefHuman:AvatarRobot  -0.01288    0.33769  60.72099
##                                               t value Pr(>|t|)    
## (Intercept)                                    70.033  < 2e-16 ***
## CongruencyIncongruent                           2.612   0.0106 *  
## BeliefHuman                                     1.602   0.1142    
## AvatarRobot                                     4.831 9.34e-06 ***
## CongruencyIncongruent:BeliefHuman              -0.126   0.9002    
## CongruencyIncongruent:AvatarRobot              -1.554   0.1253    
## BeliefHuman:AvatarRobot                         1.322   0.1913    
## CongruencyIncongruent:BeliefHuman:AvatarRobot  -0.038   0.9697    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.350                                          
## BeliefHuman -0.543  0.031                                   
## AvatarRobot -0.151  0.123  0.162                            
## CngrncyI:BH  0.054 -0.318 -0.092 -0.231                     
## CngrncyI:AR -0.040 -0.263  0.043 -0.410  0.493              
## BlfHmn:AvtR  0.117 -0.096 -0.204 -0.779  0.300  0.319       
## CngrI:BH:AR  0.031  0.203 -0.064  0.317 -0.637 -0.773 -0.408
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief + Congruency:Avatar + Belief:Avatar +
## Congruency:Belief:Avatar). The model included Congruency as random effects
## (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.37) and the part related to the fixed effects alone (marginal R2) is of 0.06.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 20.51 (95% CI [19.94, 21.08], t(5865) = 70.03,
## p < .001). Within this model:
## 
##   - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.18, 95% CI [0.30, 2.07], t(5865) = 2.61, p = 0.009; Std.
## beta = 0.39, 95% CI [0.10, 0.68])
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.43, 95% CI [-0.10, 0.96], t(5865) = 1.60, p = 0.109; Std. beta =
## 0.14, 95% CI [-0.03, 0.32])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.99, 95% CI [0.59, 1.39], t(5865) = 4.83, p < .001; Std. beta = 0.32, 95% CI
## [0.19, 0.46])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.03, 95% CI [-0.50, 0.44], t(5865) =
## -0.13, p = 0.900; Std. beta = -0.01, 95% CI [-0.17, 0.15])
##   - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.41, 95% CI [-0.92, 0.11], t(5865) =
## -1.55, p = 0.120; Std. beta = -0.13, 95% CI [-0.30, 0.03])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.35, 95% CI [-0.17, 0.86], t(5865) =
## 1.32, p = 0.186; Std. beta = 0.11, 95% CI [-0.06, 0.28])
##   - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.01, 95% CI [-0.67, 0.65],
## t(5865) = -0.04, p = 0.970; Std. beta = -4.24e-03, 95% CI [-0.22, 0.21])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))
## [1] "very strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.0109985
## [1] 0.0109985
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
Independent Samples t-Test (SRTtf by Avatar)

The mean SRTtf for the anthropomorphic avatar was 21.396 (SD = 2.754), whereas the mean for the robot avatar was 22.359 (SD = 3.227). A Welch two-samples t-test showed that the difference was statistically not significant, t(5723.4945917) = -12.3140331, p = 2.07^{-34}.

ANOVA (SRTtf by Avatar)
##               Df Sum Sq Mean Sq F value Pr(>F)    
## Avatar         1   1366    1366   151.9 <2e-16 ***
## Residuals   5883  52896       9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Shapiro-Wilk normality test
## 
## data:  aov_residuals[0:5000]
## W = 0.9889, p-value < 2.2e-16
## 
##  Kruskal-Wallis rank sum test
## 
## data:  SRTtf by Avatar
## Kruskal-Wallis chi-squared = 208.45, df = 1, p-value < 2.2e-16
## [1] TRUE
## [1] TRUE
Independent Samples t-Test (SRTtf Difference by Avatar)

The mean SRTtf Difference between congruent and incongruent trials for the anthropomorphic group was -1.112 (SD = 0.955), whereas the mean difference for the robot avatar was -0.772 (SD = 1.155). A Welch two-samples t-test showed that the difference was statistically not significant, t(116.4019224) = -1.7868517, p = 0.0766.

ANOVA (SRTtf Difference by Avatar)
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
##              Df Sum Sq Mean Sq F value Pr(>F)  
## Avatar        1    3.6   3.597   3.212 0.0756 .
## Residuals   122  136.6   1.120                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Shapiro-Wilk normality test
## 
## data:  aov_residuals[0:5000]
## W = 0.98877, p-value = 0.4067
## 
##  Kruskal-Wallis rank sum test
## 
## data:  SRTtfDiff by Avatar
## Kruskal-Wallis chi-squared = 3.7124, df = 1, p-value = 0.05401
## [1] TRUE
## [1] TRUE
Avatar (Robot)
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 505.048 21.926 111.486 23.035 0.000
CongruencyIncongruent 48.358 29.476 85.564 1.641 0.105
BeliefHuman 54.343 22.533 59.246 2.412 0.019
CongruencyIncongruent:BeliefHuman -0.545 16.485 54.215 -0.033 0.974
##                       (Intercept)             CongruencyIncongruent 
##                       505.0477092                        48.3578383 
##                       BeliefHuman CongruencyIncongruent:BeliefHuman 
##                        54.3428603                        -0.5446473
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 43.044 0.978 118.299 44.028 0.000
CongruencyIncongruent 2.201 1.395 83.753 1.578 0.118
BeliefHuman 2.453 0.954 59.256 2.571 0.013
CongruencyIncongruent:BeliefHuman -0.175 0.714 54.201 -0.244 0.808
##                       (Intercept)             CongruencyIncongruent 
##                        43.0442716                         2.2013746 
##                       BeliefHuman CongruencyIncongruent:BeliefHuman 
##                         2.4528081                        -0.1745263
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Congruency:Belief + (0 + Congruency |  
##     SubjectID) + (1 | TrialID)
##    Data: SRTData_Robot
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 20011.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5470 -0.5971 -0.0048  0.5691  7.2472 
## 
## Random effects:
##  Groups    Name                  Variance Std.Dev. Corr
##  TrialID   (Intercept)           22.11    4.702        
##  SubjectID CongruencyCongruent   11.73    3.425        
##            CongruencyIncongruent 10.27    3.205    0.91
##  Residual                        48.02    6.930        
## Number of obs: 2928, groups:  TrialID, 72; SubjectID, 61
## 
## Fixed effects:
##                                   Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                        43.0443     0.9777 118.2988  44.028   <2e-16
## CongruencyIncongruent               2.2014     1.3951  83.7531   1.578   0.1184
## BeliefHuman                         2.4528     0.9541  59.2564   2.571   0.0127
## CongruencyIncongruent:BeliefHuman  -0.1745     0.7141  54.2014  -0.244   0.8078
##                                      
## (Intercept)                       ***
## CongruencyIncongruent                
## BeliefHuman                       *  
## CongruencyIncongruent:BeliefHuman    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn
## CngrncyIncn -0.398              
## BeliefHuman -0.584  0.100       
## CngrncyI:BH  0.190 -0.307 -0.321
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency and Belief (formula: SRTtf ~ Congruency + Belief
## + Congruency:Belief). The model included Congruency as random effects (formula:
## list(~0 + Congruency | SubjectID, ~1 | TrialID)). The model's total explanatory
## power is substantial (conditional R2 = 0.36) and the part related to the fixed
## effects alone (marginal R2) is of 0.03. The model's intercept, corresponding to
## Congruency = Congruent and Belief = AI, is at 43.04 (95% CI [41.13, 44.96],
## t(2919) = 44.03, p < .001). Within this model:
## 
##   - The effect of Congruency [Incongruent] is statistically non-significant and
## positive (beta = 2.20, 95% CI [-0.53, 4.94], t(2919) = 1.58, p = 0.115; Std.
## beta = 0.25, 95% CI [-0.06, 0.56])
##   - The effect of Belief [Human] is statistically significant and positive (beta
## = 2.45, 95% CI [0.58, 4.32], t(2919) = 2.57, p = 0.010; Std. beta = 0.28, 95%
## CI [0.07, 0.49])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.17, 95% CI [-1.57, 1.23], t(2919) =
## -0.24, p = 0.807; Std. beta = -0.02, 95% CI [-0.18, 0.14])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Congruency as random effects (formula: list(~0 + Congruency | SubjectID, ~1 | TrialID))
## [1] "strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.03397302
## [1] 0.03397302
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] FALSE
## [1] TRUE
Avatar (Anthropomorphic)
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 458.136 15.411 110.995 29.728 0.000
CongruencyIncongruent 67.924 22.516 96.398 3.017 0.003
BeliefHuman 23.432 15.841 60.472 1.479 0.144
CongruencyIncongruent:BeliefHuman -0.470 15.948 60.663 -0.029 0.977
##                       (Intercept)             CongruencyIncongruent 
##                       458.1359973                        67.9235289 
##                       BeliefHuman CongruencyIncongruent:BeliefHuman 
##                        23.4315188                        -0.4698318
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 12.883 0.129 115.665 99.940 0.000
CongruencyIncongruent 0.548 0.186 87.609 2.951 0.004
BeliefHuman 0.192 0.129 60.594 1.488 0.142
CongruencyIncongruent:BeliefHuman -0.003 0.110 61.912 -0.026 0.980
##                       (Intercept)             CongruencyIncongruent 
##                       12.88259629                        0.54770443 
##                       BeliefHuman CongruencyIncongruent:BeliefHuman 
##                        0.19173801                       -0.00281953
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Congruency:Belief + (0 + Congruency |  
##     SubjectID) + (1 | TrialID)
##    Data: SRTData_Anthropomorphic
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 9168.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8812 -0.6009 -0.0038  0.5994  6.7588 
## 
## Random effects:
##  Groups    Name                  Variance Std.Dev. Corr
##  TrialID   (Intercept)           0.3641   0.6034       
##  SubjectID CongruencyCongruent   0.2152   0.4639       
##            CongruencyIncongruent 0.2763   0.5257   0.90
##  Residual                        1.1548   1.0746       
## Number of obs: 2957, groups:  TrialID, 72; SubjectID, 63
## 
## Fixed effects:
##                                    Estimate Std. Error        df t value
## (Intercept)                        12.88260    0.12890 115.66456  99.940
## CongruencyIncongruent               0.54770    0.18558  87.60900   2.951
## BeliefHuman                         0.19174    0.12883  60.59411   1.488
## CongruencyIncongruent:BeliefHuman  -0.00282    0.11042  61.91179  -0.026
##                                   Pr(>|t|)    
## (Intercept)                        < 2e-16 ***
## CongruencyIncongruent              0.00406 ** 
## BeliefHuman                        0.14185    
## CongruencyIncongruent:BeliefHuman  0.97971    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn
## CngrncyIncn -0.333              
## BeliefHuman -0.591  0.049       
## CngrncyI:BH  0.083 -0.357 -0.134
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency and Belief (formula: SRTtf ~ Congruency + Belief
## + Congruency:Belief). The model included Congruency as random effects (formula:
## list(~0 + Congruency | SubjectID, ~1 | TrialID)). The model's total explanatory
## power is substantial (conditional R2 = 0.30) and the part related to the fixed
## effects alone (marginal R2) is of 0.04. The model's intercept, corresponding to
## Congruency = Congruent and Belief = AI, is at 12.88 (95% CI [12.63, 13.14],
## t(2948) = 99.94, p < .001). Within this model:
## 
##   - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 0.55, 95% CI [0.18, 0.91], t(2948) = 2.95, p = 0.003; Std.
## beta = 0.42, 95% CI [0.14, 0.70])
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.19, 95% CI [-0.06, 0.44], t(2948) = 1.49, p = 0.137; Std. beta =
## 0.15, 95% CI [-0.05, 0.34])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -2.82e-03, 95% CI [-0.22, 0.21], t(2948) =
## -0.03, p = 0.980; Std. beta = -2.16e-03, 95% CI [-0.17, 0.16])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Congruency as random effects (formula: list(~0 + Congruency | SubjectID, ~1 | TrialID))
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 0.005071679
## [1] 0.005071679
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] FALSE
## [1] TRUE
Overt Attention Trials Only
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 450.413 17.736 122.595 25.395 0.000
CongruencyIncongruent 75.288 26.558 104.899 2.835 0.006
BeliefHuman 22.674 17.691 61.766 1.282 0.205
AvatarRobot 69.827 14.334 63.513 4.872 0.000
CongruencyIncongruent:BeliefHuman -0.689 18.273 56.415 -0.038 0.970
CongruencyIncongruent:AvatarRobot -30.590 19.538 59.741 -1.566 0.123
BeliefHuman:AvatarRobot 19.824 18.160 59.819 1.092 0.279
CongruencyIncongruent:BeliefHuman:AvatarRobot 5.604 24.879 56.890 0.225 0.823
##                                   (Intercept) 
##                                   450.4133454 
##                         CongruencyIncongruent 
##                                    75.2880384 
##                                   BeliefHuman 
##                                    22.6740467 
##                                   AvatarRobot 
##                                    69.8269011 
##             CongruencyIncongruent:BeliefHuman 
##                                    -0.6893588 
##             CongruencyIncongruent:AvatarRobot 
##                                   -30.5904151 
##                       BeliefHuman:AvatarRobot 
##                                    19.8238492 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                     5.6042587
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 24.205 0.401 123.551 60.378 0.000
CongruencyIncongruent 1.615 0.591 97.879 2.734 0.007
BeliefHuman 0.519 0.394 60.573 1.319 0.192
AvatarRobot 1.367 0.282 63.065 4.847 0.000
CongruencyIncongruent:BeliefHuman 0.001 0.361 54.318 0.003 0.998
CongruencyIncongruent:AvatarRobot -0.616 0.385 58.530 -1.601 0.115
BeliefHuman:AvatarRobot 0.442 0.357 59.360 1.239 0.220
CongruencyIncongruent:BeliefHuman:AvatarRobot -0.043 0.490 55.725 -0.087 0.931
##                                   (Intercept) 
##                                  24.204691709 
##                         CongruencyIncongruent 
##                                   1.615132343 
##                                   BeliefHuman 
##                                   0.519332902 
##                                   AvatarRobot 
##                                   1.367125657 
##             CongruencyIncongruent:BeliefHuman 
##                                   0.001036391 
##             CongruencyIncongruent:AvatarRobot 
##                                  -0.616454267 
##                       BeliefHuman:AvatarRobot 
##                                   0.441909681 
## CongruencyIncongruent:BeliefHuman:AvatarRobot 
##                                  -0.042514925
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief + Congruency:Avatar +  
##     Belief:Avatar + Congruency:Belief:Avatar + (0 + Congruency +  
##     Avatar + Congruency:Avatar | SubjectID) + (1 | TrialID)
##    Data: SRTDataOA
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 22073.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4662 -0.6065 -0.0091  0.5975  6.7734 
## 
## Random effects:
##  Groups    Name                              Variance Std.Dev. Corr       
##  TrialID   (Intercept)                       3.6111   1.9003              
##  SubjectID CongruencyCongruent               1.7448   1.3209              
##            CongruencyIncongruent             2.1894   1.4797    0.91      
##            AvatarRobot                       0.7968   0.8926   -0.01  0.07
##            CongruencyIncongruent:AvatarRobot 0.5326   0.7298   -0.47 -0.52
##  Residual                                    9.6594   3.1080              
##       
##       
##       
##       
##       
##  -0.30
##       
## Number of obs: 4235, groups:  TrialID, 72; SubjectID, 64
## 
## Fixed effects:
##                                                 Estimate Std. Error         df
## (Intercept)                                    24.204692   0.400888 123.550678
## CongruencyIncongruent                           1.615132   0.590787  97.878588
## BeliefHuman                                     0.519333   0.393785  60.572526
## AvatarRobot                                     1.367126   0.282030  63.065353
## CongruencyIncongruent:BeliefHuman               0.001036   0.361346  54.318432
## CongruencyIncongruent:AvatarRobot              -0.616454   0.385085  58.529947
## BeliefHuman:AvatarRobot                         0.441910   0.356551  59.360323
## CongruencyIncongruent:BeliefHuman:AvatarRobot  -0.042515   0.489600  55.725207
##                                               t value Pr(>|t|)    
## (Intercept)                                    60.378  < 2e-16 ***
## CongruencyIncongruent                           2.734  0.00743 ** 
## BeliefHuman                                     1.319  0.19219    
## AvatarRobot                                     4.847 8.51e-06 ***
## CongruencyIncongruent:BeliefHuman               0.003  0.99772    
## CongruencyIncongruent:AvatarRobot              -1.601  0.11480    
## BeliefHuman:AvatarRobot                         1.239  0.22008    
## CongruencyIncongruent:BeliefHuman:AvatarRobot  -0.087  0.93111    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.370                                          
## BeliefHuman -0.593  0.089                                   
## AvatarRobot -0.221  0.151  0.224                            
## CngrncyI:BH  0.143 -0.381 -0.221 -0.247                     
## CngrncyI:AR  0.021 -0.305 -0.021 -0.432  0.498              
## BlfHmn:AvtR  0.174 -0.119 -0.270 -0.790  0.305  0.341       
## CngrI:BH:AR -0.016  0.240  0.009  0.339 -0.626 -0.786 -0.425
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief + Congruency:Avatar + Belief:Avatar +
## Congruency:Belief:Avatar). The model included Congruency as random effects
## (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.36) and the part related to the fixed effects alone (marginal R2) is of 0.07.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 24.20 (95% CI [23.42, 24.99], t(4215) = 60.38,
## p < .001). Within this model:
## 
##   - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.62, 95% CI [0.46, 2.77], t(4215) = 2.73, p = 0.006; Std.
## beta = 0.41, 95% CI [0.11, 0.70])
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.52, 95% CI [-0.25, 1.29], t(4215) = 1.32, p = 0.187; Std. beta =
## 0.13, 95% CI [-0.06, 0.32])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 1.37, 95% CI [0.81, 1.92], t(4215) = 4.85, p < .001; Std. beta = 0.34, 95% CI
## [0.20, 0.48])
##   - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and positive (beta = 1.04e-03, 95% CI [-0.71, 0.71], t(4215) =
## 2.87e-03, p = 0.998; Std. beta = 2.60e-04, 95% CI [-0.18, 0.18])
##   - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.62, 95% CI [-1.37, 0.14], t(4215) =
## -1.60, p = 0.109; Std. beta = -0.15, 95% CI [-0.34, 0.03])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.44, 95% CI [-0.26, 1.14], t(4215) =
## 1.24, p = 0.215; Std. beta = 0.11, 95% CI [-0.06, 0.29])
##   - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.04, 95% CI [-1.00, 0.92],
## t(4215) = -0.09, p = 0.931; Std. beta = -0.01, 95% CI [-0.25, 0.23])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))
## [1] "very strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.01885772
## [1] 0.01885772
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
No Overt Attention Trials Only
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 419.776 56.437 29.786 7.438 0.000
CongruencyIncongruent 67.357 32.418 39.139 2.078 0.044
BeliefHuman 45.403 38.604 35.231 1.176 0.247
AvatarRobot 104.009 28.261 45.438 3.680 0.001
CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 38.375 55.429 26.267 0.692 0.495
CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 23.621 40.228 46.868 0.587 0.560
CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 22.371 29.742 37.620 0.752 0.457
CongruencyCongruent:BeliefAI:AvatarRobot 3.086 34.206 16.548 0.090 0.929
##                                           (Intercept) 
##                                            419.776266 
##                                 CongruencyIncongruent 
##                                             67.356673 
##                                           BeliefHuman 
##                                             45.403465 
##                                           AvatarRobot 
##                                            104.009093 
##    CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 
##                                             38.375114 
##  CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 
##                                             23.621054 
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 
##                                             22.370758 
##              CongruencyCongruent:BeliefAI:AvatarRobot 
##                                              3.085896

## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 14.673 0.518 40.722 28.350 0.000
CongruencyIncongruent 0.609 0.341 62.518 1.785 0.079
BeliefHuman 0.470 0.338 36.530 1.391 0.173
AvatarRobot 0.849 0.257 66.203 3.300 0.002
CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 0.316 0.506 34.635 0.626 0.536
CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 0.292 0.365 69.804 0.798 0.427
CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 0.128 0.278 62.927 0.461 0.646
CongruencyCongruent:BeliefAI:AvatarRobot 0.099 0.322 23.368 0.308 0.761
##                                           (Intercept) 
##                                           14.67314213 
##                                 CongruencyIncongruent 
##                                            0.60879729 
##                                           BeliefHuman 
##                                            0.46985484 
##                                           AvatarRobot 
##                                            0.84895192 
##    CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 
##                                            0.31631800 
##  CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 
##                                            0.29169776 
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 
##                                            0.12835394 
##              CongruencyCongruent:BeliefAI:AvatarRobot 
##                                            0.09919277
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief:Avatar +  
##     (0 + Congruency + Avatar + Congruency:Avatar | SubjectID) +  
##     (1 | TrialID)
##    Data: SRTDataOANo
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 6151.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.0248 -0.5575  0.0087  0.5492  6.3806 
## 
## Random effects:
##  Groups    Name                              Variance Std.Dev. Corr       
##  TrialID   (Intercept)                       0.8408   0.9170              
##  SubjectID CongruencyCongruent               0.3069   0.5540              
##            CongruencyIncongruent             0.2471   0.4971    0.87      
##            AvatarRobot                       0.4004   0.6327   -0.23  0.16
##            CongruencyIncongruent:AvatarRobot 0.1669   0.4085    0.17  0.03
##  Residual                                    2.0432   1.4294              
##       
##       
##       
##       
##       
##  -0.83
##       
## Number of obs: 1650, groups:  TrialID, 72; SubjectID, 64
## 
## Fixed effects:
##                                                       Estimate Std. Error
## (Intercept)                                           14.67314    0.51758
## CongruencyIncongruent                                  0.60880    0.34113
## BeliefHuman                                            0.46985    0.33767
## AvatarRobot                                            0.84895    0.25723
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic     0.31632    0.50558
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic   0.29170    0.36533
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic  0.12835    0.27830
## CongruencyCongruent:BeliefAI:AvatarRobot               0.09919    0.32249
##                                                             df t value Pr(>|t|)
## (Intercept)                                           40.72183  28.350  < 2e-16
## CongruencyIncongruent                                 62.51847   1.785  0.07917
## BeliefHuman                                           36.52994   1.391  0.17250
## AvatarRobot                                           66.20328   3.300  0.00156
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic    34.63458   0.626  0.53564
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic  69.80440   0.798  0.42731
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 62.92680   0.461  0.64624
## CongruencyCongruent:BeliefAI:AvatarRobot              23.36846   0.308  0.76113
##                                                          
## (Intercept)                                           ***
## CongruencyIncongruent                                 .  
## BeliefHuman                                              
## AvatarRobot                                           ** 
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic       
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic     
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic    
## CongruencyCongruent:BeliefAI:AvatarRobot                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) CngrnI BlfHmn AvtrRb CC:BAI:AA CI:BAI CC:BH:
## CngrncyIncn -0.588                                             
## BeliefHuman -0.820  0.351                                      
## AvatarRobot -0.783  0.422  0.509                               
## CngC:BAI:AA -0.932  0.506  0.794  0.802                        
## CngI:BAI:AA -0.787  0.300  0.722  0.701  0.820                 
## CngrC:BH:AA -0.731  0.487  0.374  0.809  0.750     0.568       
## CngC:BAI:AR -0.767  0.457  0.734  0.461  0.793     0.647  0.529
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## Random effect variances not available. Returned R2 does not account for random effects.
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## Random effect variances not available. Returned R2 does not account for random effects.
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief:Avatar). The model included Congruency as
## random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar |
## SubjectID, ~1 | TrialID)). The model's explanatory power related to the fixed
## effects alone (marginal R2) is 0.09. The model's intercept, corresponding to
## Congruency = Congruent, Belief = AI and Avatar = Anthropomorphic, is at 14.67
## (95% CI [13.66, 15.69], t(1630) = 28.35, p < .001). Within this model:
## 
##   - The effect of Congruency [Incongruent] is statistically non-significant and
## positive (beta = 0.61, 95% CI [-0.06, 1.28], t(1630) = 1.78, p = 0.075; Std.
## beta = 0.35, 95% CI [-0.03, 0.74])
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.47, 95% CI [-0.19, 1.13], t(1630) = 1.39, p = 0.164; Std. beta =
## 0.27, 95% CI [-0.11, 0.65])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.85, 95% CI [0.34, 1.35], t(1630) = 3.30, p < .001; Std. beta = 0.49, 95% CI
## [0.20, 0.78])
##   - The effect of CongruencyCongruent × BeliefAI × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.32, 95% CI [-0.68, 1.31],
## t(1630) = 0.63, p = 0.532; Std. beta = 0.18, 95% CI [-0.39, 0.75])
##   - The effect of Congruency [Incongruent] × BeliefAI × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.29, 95% CI [-0.42, 1.01],
## t(1630) = 0.80, p = 0.425; Std. beta = 0.17, 95% CI [-0.24, 0.58])
##   - The effect of CongruencyCongruent × Belief [Human] × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.13, 95% CI [-0.42, 0.67],
## t(1630) = 0.46, p = 0.645; Std. beta = 0.07, 95% CI [-0.24, 0.39])
##   - The effect of CongruencyCongruent × BeliefAI × Avatar [Robot] is
## statistically non-significant and positive (beta = 0.10, 95% CI [-0.53, 0.73],
## t(1630) = 0.31, p = 0.758; Std. beta = 0.06, 95% CI [-0.31, 0.42])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 7.505645e-08
## [1] 7.505645e-08
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 6.118933e-06
## [1] 6.118933e-06
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 6.118933e-06
## [1] 6.118933e-06
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 4.435249e-06
## [1] 4.435249e-06
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## boundary (singular) fit: see help('isSingular')
## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

Influence of CATI Scores on SRT

## 
##  Shapiro-Wilk normality test
## 
## data:  SRTtfCATI$Diff_SRTtfMean[0:5000]
## W = 0.99154, p-value = 0.655
## 
##  Shapiro-Wilk normality test
## 
## data:  SRTtfCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155
## [1] 0.5327362
## [1] 0.4711401

##                       CATI Diff_SRTtfMean
## CATI            1.00000000    -0.07606236
## Diff_SRTtfMean -0.07606236     1.00000000

## 
##  Spearman's rank correlation rho
## 
## data:  SRTtfCATI$Diff_SRTtfMean and SRTtfCATI$CATI
## S = 350969, p-value = 0.2479
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.1045442

SRT Summary

All Trials
## `summarise()` has grouped output by 'Avatar'. You can override using the
## `.groups` argument.
## [1] TRUE
## [1] TRUE
Overt Attention Trials Only
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## [1] TRUE
## [1] TRUE
No Overt Attention Trials Only
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## [1] TRUE
## [1] TRUE

Initiator Trials

## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.

Accuracy

Plot

Generalised Linear Mixed Effect Model for Initiator Accuracy

Estimate Std. Error z value Pr(>|z|)
(Intercept) 7.101 1.074 6.614 0.000
BeliefHuman 0.692 1.029 0.672 0.502
AvatarRobot -1.885 1.115 -1.690 0.091
BeliefHuman:AvatarRobot -0.644 1.168 -0.551 0.582
##             (Intercept)             BeliefHuman             AvatarRobot 
##               7.1007093               0.6915022              -1.8847620 
## BeliefHuman:AvatarRobot 
##              -0.6437033
## Error in file(file, if (append) "a" else "w"): cannot open the connection
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: CorrectIncorrect ~ Belief + Avatar + Belief:Avatar + (1 + Belief +  
##     Avatar | SubjectID) + (1 | TrialID)
##    Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
##      AIC      BIC   logLik deviance df.resid 
##    924.6   1001.9   -451.3    902.6     8356 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -12.3777   0.0228   0.0594   0.0868   1.8279 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev. Corr       
##  TrialID   (Intercept) 0.8156   0.9031              
##  SubjectID (Intercept) 6.7835   2.6045              
##            BeliefHuman 2.2803   1.5101   -0.19      
##            AvatarRobot 7.6515   2.7661   -0.98  0.00
## Number of obs: 8367, groups:  TrialID, 72; SubjectID, 65
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               7.1007     1.0736   6.614 3.75e-11 ***
## BeliefHuman               0.6915     1.0292   0.672   0.5017    
## AvatarRobot              -1.8848     1.1155  -1.690   0.0911 .  
## BeliefHuman:AvatarRobot  -0.6437     1.1681  -0.551   0.5816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) BlfHmn AvtrRb
## BeliefHuman -0.473              
## AvatarRobot -0.938  0.490       
## BlfHmn:AvtR  0.418 -0.912 -0.527
## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict CorrectIncorrect with Belief and Avatar (formula: CorrectIncorrect ~
## Belief + Avatar + Belief:Avatar). The model included Belief as random effects
## (formula: list(~1 + Belief + Avatar | SubjectID, ~1 | TrialID)). The model's
## total explanatory power is substantial (conditional R2 = 0.65) and the part
## related to the fixed effects alone (marginal R2) is of 0.14. The model's
## intercept, corresponding to Belief = AI and Avatar = Anthropomorphic, is at
## 7.10 (95% CI [5.00, 9.21], p < .001). Within this model:
## 
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.69, 95% CI [-1.33, 2.71], p = 0.502; Std. beta = 0.69, 95% CI [-1.33,
## 2.71])
##   - The effect of Avatar [Robot] is statistically non-significant and negative
## (beta = -1.88, 95% CI [-4.07, 0.30], p = 0.091; Std. beta = -1.88, 95% CI
## [-4.07, 0.30])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.64, 95% CI [-2.93, 1.65], p = 0.582;
## Std. beta = -0.64, 95% CI [-2.93, 1.65])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.
## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 | TrialID))
## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)
## [1] 1
## Error in file(file, if (append) "a" else "w"): cannot open the connection
## [1] 1
## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)
## [1] 1
## Error in file(file, if (append) "a" else "w"): cannot open the connection
## [1] 1
## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)
## [1] 1
## Error in file(file, if (append) "a" else "w"): cannot open the connection
## [1] 1
## [1] FALSE
## [1] FALSE
## [1] FALSE
## [1] FALSE
## [1] FALSE
## [1] FALSE
## [1] FALSE
## [1] FALSE

Accuracy Summary

## [1] TRUE
## [1] TRUE

Overt Attention

Frequency of Initiator Overt Attention

Plot
Load Data and Identify Factors

Linear Mixed Effects Models
Load Data and Identify Factors
## boundary (singular) fit: see help('isSingular')
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.406 0.275 5.120 0.000
BeliefHuman 0.322 0.380 0.847 0.397
AvatarRobot 0.199 0.136 1.458 0.145
## (Intercept) BeliefHuman AvatarRobot 
##   1.4061579   0.3215809   0.1986315
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: iOAFAll ~ Belief + Avatar + (1 + Belief + Avatar | SubjectID) +  
##     (1 + Belief | TrialID)
##    Data: UseableInitData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
##      AIC      BIC   logLik deviance df.resid 
##   7441.5   7525.7  -3708.7   7417.5     8252 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.1151  0.0907  0.3142  0.5037  2.0203 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev. Corr       
##  TrialID   (Intercept) 0.000000 0.00000             
##            BeliefHuman 0.001356 0.03682   NaN       
##  SubjectID (Intercept) 2.069187 1.43847             
##            BeliefHuman 1.180184 1.08636  -0.14      
##            AvatarRobot 0.668626 0.81770  -0.37 -0.03
## Number of obs: 8264, groups:  TrialID, 72; SubjectID, 65
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.4062     0.2746   5.120 3.05e-07 ***
## BeliefHuman   0.3216     0.3799   0.847    0.397    
## AvatarRobot   0.1986     0.1363   1.458    0.145    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) BlfHmn
## BeliefHuman -0.667       
## AvatarRobot -0.242 -0.056
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## Random effect variances not available. Returned R2 does not account for random effects.
## boundary (singular) fit: see help('isSingular')
## Random effect variances not available. Returned R2 does not account for random effects.
## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict iOAFAll with Belief and Avatar (formula: iOAFAll ~ Belief + Avatar).
## The model included Belief as random effects (formula: list(~1 + Belief + Avatar
## | SubjectID, ~1 + Belief | TrialID)). The model's explanatory power related to
## the fixed effects alone (marginal R2) is 0.01. The model's intercept,
## corresponding to Belief = AI and Avatar = Anthropomorphic, is at 1.41 (95% CI
## [0.87, 1.94], p < .001). Within this model:
## 
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.32, 95% CI [-0.42, 1.07], p = 0.397; Std. beta = 0.32, 95% CI [-0.42,
## 1.07])
##   - The effect of Avatar [Robot] is statistically non-significant and positive
## (beta = 0.20, 95% CI [-0.07, 0.47], p = 0.145; Std. beta = 0.20, 95% CI [-0.07,
## 0.47])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.
## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 + Belief | TrialID))
## boundary (singular) fit: see help('isSingular')
## [1] "very strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.01563404
## [1] 0.01563404
## boundary (singular) fit: see help('isSingular')
## [1] "very strong evidence against"
## (Rules: jeffreys1961)
## [1] 0.02970183
## [1] 0.02970183
## boundary (singular) fit: see help('isSingular')
## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

Initiator Total Overt Attention

Plot
Load Data and Identify Factors

##### Linear Mixed Effects Models

Load Data and Identify Factors
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 926.484 104.169 68.282 8.894 0.000
BeliefHuman 125.535 135.263 64.529 0.928 0.357
AvatarRobot 74.183 86.726 62.269 0.855 0.396
BeliefHuman:AvatarRobot -97.580 109.600 56.466 -0.890 0.377
##             (Intercept)             BeliefHuman             AvatarRobot 
##               926.48382               125.53531                74.18283 
## BeliefHuman:AvatarRobot 
##               -97.57970

## boundary (singular) fit: see help('isSingular')
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 8.087 0.112 31.367 71.906 0.00
BeliefHuman 0.090 0.150 61.244 0.602 0.55
AvatarRobot -0.019 0.065 51.599 -0.294 0.77
## (Intercept) BeliefHuman AvatarRobot 
##  8.08702120  0.09007677 -0.01921343
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: TOAT ~ Belief + Avatar + (1 + Belief + Avatar | SubjectID) +  
##     (1 + Belief | TrialID)
##    Data: iTotalOAData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 11693.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.1385 -0.5624  0.0448  0.5502  4.1781 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev. Corr       
##  TrialID   (Intercept) 0.01475  0.1214              
##            BeliefHuman 0.01398  0.1182   -1.00      
##  SubjectID (Intercept) 0.32876  0.5734              
##            BeliefHuman 0.40210  0.6341   -0.47      
##            AvatarRobot 0.16736  0.4091   -0.42  0.20
##  Residual              1.01494  1.0074              
## Number of obs: 4002, groups:  TrialID, 72; SubjectID, 65
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  8.08702    0.11247 31.36742  71.906   <2e-16 ***
## BeliefHuman  0.09008    0.14970 61.24401   0.602     0.55    
## AvatarRobot -0.01921    0.06540 51.59866  -0.294     0.77    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) BlfHmn
## BeliefHuman -0.698       
## AvatarRobot -0.336  0.095
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## Random effect variances not available. Returned R2 does not account for random effects.
## boundary (singular) fit: see help('isSingular')
## Random effect variances not available. Returned R2 does not account for random effects.
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict TOAT with Belief and Avatar (formula: TOAT ~ Belief + Avatar). The
## model included Belief as random effects (formula: list(~1 + Belief + Avatar |
## SubjectID, ~1 + Belief | TrialID)). The model's explanatory power related to
## the fixed effects alone (marginal R2) is 1.95e-03. The model's intercept,
## corresponding to Belief = AI and Avatar = Anthropomorphic, is at 8.09 (95% CI
## [7.87, 8.31], t(3989) = 71.91, p < .001). Within this model:
## 
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.09, 95% CI [-0.20, 0.38], t(3989) = 0.60, p = 0.547; Std. beta =
## 0.08, 95% CI [-0.17, 0.33])
##   - The effect of Avatar [Robot] is statistically non-significant and negative
## (beta = -0.02, 95% CI [-0.15, 0.11], t(3989) = -0.29, p = 0.769; Std. beta =
## -0.02, 95% CI [-0.13, 0.09])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 + Belief | TrialID))
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 7.804832e-07
## [1] 7.804832e-07
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 7.804832e-07
## [1] 7.804832e-07
## boundary (singular) fit: see help('isSingular')
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 6.573804e-09
## [1] 6.573804e-09
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

Initiator Overt Attention Before Partner Response

Plot
Load Data and Identify Factors

##### Linear Mixed Effects Models

Load Data and Identify Factors
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 819.066 102.218 69.309 8.013 0.000
BeliefHuman 116.751 131.098 64.494 0.891 0.376
AvatarRobot 54.845 90.275 61.712 0.608 0.546
BeliefHuman:AvatarRobot -126.744 112.689 55.783 -1.125 0.266
##             (Intercept)             BeliefHuman             AvatarRobot 
##               819.06647               116.75052                54.84452 
## BeliefHuman:AvatarRobot 
##              -126.74361
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 5.937 0.080 66.185 74.286 0.000
BeliefHuman 0.111 0.103 61.687 1.076 0.286
AvatarRobot 0.007 0.070 61.394 0.096 0.924
BeliefHuman:AvatarRobot -0.112 0.088 55.718 -1.272 0.209
##             (Intercept)             BeliefHuman             AvatarRobot 
##             5.936890746             0.110827056             0.006739816 
## BeliefHuman:AvatarRobot 
##            -0.111642861
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iOABRT ~ Belief + Avatar + Belief:Avatar + (1 + Avatar | SubjectID) +  
##     (1 | TrialID)
##    Data: iOABRespData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 7163
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7039 -0.5870  0.0357  0.5729  4.0256 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev. Corr 
##  TrialID   (Intercept) 0.003524 0.05936       
##  SubjectID (Intercept) 0.135700 0.36838       
##            AvatarRobot 0.064180 0.25334  -0.20
##  Residual              0.408067 0.63880       
## Number of obs: 3550, groups:  TrialID, 72; SubjectID, 65
## 
## Fixed effects:
##                         Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)              5.93689    0.07992 66.18480  74.286   <2e-16 ***
## BeliefHuman              0.11083    0.10296 61.68711   1.076    0.286    
## AvatarRobot              0.00674    0.07007 61.39397   0.096    0.924    
## BeliefHuman:AvatarRobot -0.11164    0.08775 55.71765  -1.272    0.209    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) BlfHmn AvtrRb
## BeliefHuman -0.770              
## AvatarRobot -0.375  0.291       
## BlfHmn:AvtR  0.299 -0.348 -0.799
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict iOABRT with Belief and Avatar (formula: iOABRT ~ Belief + Avatar +
## Belief:Avatar). The model included Avatar as random effects (formula: list(~1 +
## Avatar | SubjectID, ~1 | TrialID)). The model's total explanatory power is
## substantial (conditional R2 = 0.28) and the part related to the fixed effects
## alone (marginal R2) is of 4.27e-03. The model's intercept, corresponding to
## Belief = AI and Avatar = Anthropomorphic, is at 5.94 (95% CI [5.78, 6.09],
## t(3541) = 74.29, p < .001). Within this model:
## 
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.11, 95% CI [-0.09, 0.31], t(3541) = 1.08, p = 0.282; Std. beta =
## 0.15, 95% CI [-0.12, 0.42])
##   - The effect of Avatar [Robot] is statistically non-significant and positive
## (beta = 6.74e-03, 95% CI [-0.13, 0.14], t(3541) = 0.10, p = 0.923; Std. beta =
## 9.03e-03, 95% CI [-0.17, 0.19])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.11, 95% CI [-0.28, 0.06], t(3541) =
## -1.27, p = 0.203; Std. beta = -0.15, 95% CI [-0.38, 0.08])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Avatar as random effects (formula: list(~1 + Avatar | SubjectID, ~1 | TrialID))
## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)
## [1] 1
## [1] 1
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 0.008235511
## [1] 0.008235511
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

Initiator Overt Attention After Partner Response

Plot
Load Data and Identify Factors

Linear Mixed Effects Models
Load Data and Identify Factors
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 297.819 8.666 109.348 34.365 0.000
BeliefHuman 0.994 6.266 49.792 0.159 0.875
AvatarRobot 60.035 7.635 69.127 7.863 0.000
BeliefHuman:AvatarRobot 6.829 9.746 63.893 0.701 0.486
##             (Intercept)             BeliefHuman             AvatarRobot 
##             297.8194411               0.9939506              60.0352097 
## BeliefHuman:AvatarRobot 
##               6.8287011
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 13.056 0.119 115.046 110.105 0.000
BeliefHuman 0.012 0.099 50.144 0.124 0.902
AvatarRobot 0.762 0.100 64.121 7.605 0.000
BeliefHuman:AvatarRobot 0.102 0.127 58.668 0.805 0.424
##             (Intercept)             BeliefHuman             AvatarRobot 
##             13.05551772              0.01223464              0.76245916 
## BeliefHuman:AvatarRobot 
##              0.10238862
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## ResponseT ~ Belief + Avatar + Belief:Avatar + (1 + Avatar | SubjectID) +  
##     (1 | TrialID)
##    Data: iOAResponseData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
## 
## REML criterion at convergence: 9617.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.9511 -0.2891  0.1889  0.5297  4.0254 
## 
## Random effects:
##  Groups    Name        Variance Std.Dev. Corr
##  TrialID   (Intercept) 0.58079  0.7621       
##  SubjectID (Intercept) 0.06941  0.2635       
##            AvatarRobot 0.08716  0.2952   0.59
##  Residual              1.38139  1.1753       
## Number of obs: 2939, groups:  TrialID, 72; SubjectID, 65
## 
## Fixed effects:
##                          Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)              13.05552    0.11857 115.04587 110.105  < 2e-16 ***
## BeliefHuman               0.01223    0.09871  50.14393   0.124    0.902    
## AvatarRobot               0.76246    0.10025  64.12123   7.605 1.58e-10 ***
## BeliefHuman:AvatarRobot   0.10239    0.12712  58.66794   0.805    0.424    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) BlfHmn AvtrRb
## BeliefHuman -0.511              
## AvatarRobot -0.121  0.146       
## BlfHmn:AvtR  0.095 -0.137 -0.789
## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict ResponseT with Belief and Avatar (formula: ResponseT ~ Belief + Avatar
## + Belief:Avatar). The model included Avatar as random effects (formula: list(~1
## + Avatar | SubjectID, ~1 | TrialID)). The model's total explanatory power is
## substantial (conditional R2 = 0.40) and the part related to the fixed effects
## alone (marginal R2) is of 0.07. The model's intercept, corresponding to Belief
## = AI and Avatar = Anthropomorphic, is at 13.06 (95% CI [12.82, 13.29], t(2930)
## = 110.10, p < .001). Within this model:
## 
##   - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.01, 95% CI [-0.18, 0.21], t(2930) = 0.12, p = 0.901; Std. beta =
## 8.06e-03, 95% CI [-0.12, 0.14])
##   - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.76, 95% CI [0.57, 0.96], t(2930) = 7.61, p < .001; Std. beta = 0.50, 95% CI
## [0.37, 0.63])
##   - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.10, 95% CI [-0.15, 0.35], t(2930) =
## 0.81, p = 0.421; Std. beta = 0.07, 95% CI [-0.10, 0.23])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.
## The model included Avatar as random effects (formula: list(~1 + Avatar | SubjectID, ~1 | TrialID))
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 0
## [1] 0
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 0
## [1] 0
## [1] "extreme evidence against"
## (Rules: jeffreys1961)
## [1] 0
## [1] 0
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE
## [1] TRUE

ANOVA for Total Overt Attention

## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
##             Df   Sum Sq Mean Sq F value Pr(>F)
## Belief       1    64430   64430   0.321  0.573
## Residuals   63 12662393  200990
## 
##  Shapiro-Wilk normality test
## 
## data:  aov_residuals
## W = 0.87774, p-value = 1.115e-05
## 
##  Kruskal-Wallis rank sum test
## 
## data:  MeanTotalOA by Belief
## Kruskal-Wallis chi-squared = 0.38768, df = 1, p-value = 0.5335
## [1] TRUE
## [1] TRUE

Overt Attention Summary

Frequency of Initiator Overt Attention
## [1] TRUE
## [1] TRUE
Initiator Total Overt Attention
## [1] TRUE
## [1] TRUE
Initiator Overt Attention Before Partner Response
## [1] TRUE
## [1] TRUE
Initiator Overt Attention After Partner Response
## [1] TRUE
## [1] TRUE